THE EFFECT OF CRITICAL LEVELS ON 3D OROGRAPHIC FLOWS - LINEAR REGIME

The effect of a critical level on airflow past an isolated axially sym metric obstacle is investigated in the small-amplitude hydrostatic lim it for mean flows with linear negative shear. Only flows with mean Ric hardson numbers (Ri) greater or equal to 1/4 are considered. The autho rs examine the problem using the linear, steady-state, inviscid, dynam ic equations, which are well known to exhibit a singular behavior at c ritical levels, as well as a numerical model that has the capability o f capturing both nonlinear and dissipative effects where these are sig nificant. Linear theory predicts the 3D wave pattern with individual w aves that are confined to paraboloidal envelopes below the critical le vel and strongly attenuated and directionally filtered above it. Asymp totic solutions for the wave field far from the mountain and below the critical level show large shear-induced modifications in the proximit y of the critical level, where wave envelopes quickly widen with heigh t. Above the critical level, the perturbation field consists mainly of waves with wavefronts perpendicular to the mean flow direction. A clo sed-form analytic formula for the mountain-wave drag, which is equally valid for mean flows with positive and negative shear, predicts a dra g that is smaller than in the uniform wind case. In the limit of Ri SE arrow 1/4, in which linear theory predicts zero drag for an infinite ridge, drag on an axisymmetric mountain is nonzero. Numerical simulati ons with an anelastic, nonhydrostatic model confirm and qualify the an alytic results. They indicate that the linear regime, in which analyti c solutions are valid everywhere except in the vicinity of the critica l level, exists for a range of mountain heights given Ri > 1. For Ri S E arrow 1/4 this same regime is difficult to achieve, as the flow is e xtremely sensitive to nonlinearities introduced through the lower boun dary forcing that induce strong nonlinear effects near the critical le vel. Even well within the linear regime, flow in the vicinity of a cri tical level is dissipative in nature as evidenced by the development o f a potential vorticity doubler.